17
votes
Accepted
What is a "hanging node" in the finite element meshing?
The following picture illustrates a mesh with a hanging node and a mesh containing no hanging node:
Usually with a finite element mesh the vertices are shared with their other neighbouring elements, ...
- 1,879
10
votes
Why FVM can handle unstructured meshes while FDM cannot?
The difference between finite volumes and finite differences is really more about the form of the equations solved. In typical FV methods, the conservative form is ...
- 534
9
votes
Accepted
Algorithm to find boundary faces of mesh
First, create a list of faces in the mesh. From there you should be able to create a map from faces to tets, as each face must belong to either one or two tets. The faces that belong to only one tet ...
- 981
9
votes
Accepted
Library for generating Discontinuous Galerkin FEM mesh
You are confused about different concepts. A mesh is really just a collection of cells defined by the vertices of the mesh and which vertices together form each cell. Consequently, a mesh is an ...
- 54.2k
8
votes
Accepted
Unstructured mesh vs hybrid structured/unstructured for numerical simulations
In my opinion, it is not a good neither a bad mesh. It clearly depends on the PDE you are considering.
The finite space to which the PDE is projected is your mesh, where your operators, e.g. $\vec{\...
- 1,628
7
votes
Accepted
3D contour mesh computation
I think you could use the "marching cubes" algorithm. If memory serves, it requires a grid of samples as input, so at the very least you should be able to sample your function and run the algorithm as-...
- 4,822
7
votes
Accepted
Is there any open-source code for a hybrid 2D mesh (triangles and quadrilaterals)?
You can use Gmsh for this purpose. I show an example below.
...
- 8,370
6
votes
Accepted
Unreasonably large deviation in calculations of mean curvature in different algorithms
First of all remember that curvatures, being 2nd order values, can be really sensitive to even very small variations.
Moreover, we are speaking about computing differential values in a discrete ...
- 176
5
votes
Accepted
Relationship between number of nodes, elements and sides in a triangular 2D mesh
Yes there is a relationship, the Euler characteristic:
For a 2-dimensional orientable manifold with boundaries embedded in $\mathbb{R}^3$, the Euler characteristic is
$\chi = V - E + F = 2 - 2g - b$
...
- 166
5
votes
Commonly-used metrics to quantify the irregularity of a triangular mesh
I do not think that there exists an answer to this question in general, because it all depends on the intended use for the mesh. For instance, if you are doing computational fluid dynamics, you may ...
- 2,305
5
votes
Accepted
Commonly-used metrics to quantify the irregularity of a triangular mesh
As @Nicoguaro and @Paul have said in the comments to the question post, there are a great many ways to do this kind of thing, and I'm not sure if there is a single "best" approach.
From a review ...
- 534
5
votes
Accepted
Resources on mesh generation for finite element methods
Starting a community answer, in line with your model question
Mesh Generation
Mesh Generation: Application to Finite Elements (P.-L. George and P. Frey) Hermes, Lyon, 2000. A clear primer on the core ...
5
votes
Accepted
Creating a proper quad-mesh in GMSH for an "I"-shaped geometry
So, by default and without recombination to quads (comment out Recombine Surface {1}), GMSH creates a mesh like the one in the left part of the picture. And by ...
- 8,602
5
votes
3D contour mesh computation
In addition to the voxel-based approach that rchilton suggests, you could also look at Delaunay-type algorithms. For example, the Computational Geometry Algorithms Library (CGAL) has some built-in ...
- 10.1k
5
votes
Minimum number of elements (mesh size) for electromagnetic simulation
The Maxwell system is a wave equation at heart, so your ansatz (the space where you seek solutions, the combination of your mesh and basis functions) must be able to faithfully represent waves. The ...
- 4,822
4
votes
Accepted
From edge-vertex connectivty to face-vertex connectivity?
As noted in the comments, your problem doesn't seem quite solvable as stated. However, if you include the assumption that each node has a 2D coordinate associated with it, then it is solvable. With ...
- 1,522
4
votes
Accepted
Determinant of jacobian matrix
The determinant of the Jacobian, as a determinant changes its sign when odd permutations of columns (or rows) are applied.
Imagine, for simplicity a two dimensional case in which the reference ...
- 1,628
4
votes
Accepted
Meshing options to generate number of the sides of and element (tetgen-triangle)
I have implemented a method that works pretty well for reconstructing edge information in surfacic meshes (or facet information in volumetric meshes), but I am working in C++. I'll try to explain that ...
- 2,305
4
votes
Accepted
Using Gmsh to create a mesh with zero thickness (quad) interface elements
One way to do it might be to create an internal Line Loop in the input file where the crack originates. To do this, you would create 2 points at each end of the crack in your .geo file (say, points 1,...
- 1,522
4
votes
Accepted
Combined translational and rotational meshing in gmsh
I cannot visualize your geometry properly using Gmsh, or export it. I generated something similar using FreeCAD. Maybe you can modify this script for your purposes.
...
- 8,370
4
votes
How can I coarsen a mesh in Gmsh when 'Mesh options' include 'Refine by splitting' but nothing about coarsening?
To create a coarser mesh, you can set the characteristic length globally to a larger value, e.g.,
...
- 558
4
votes
Accepted
Definition of Lagrange nodes in Gmsh
I think you've got slightly the wrong end of the stick from the documentation. As with a lot of other software in the area, GMSH started out with low order, hard coded numberings. These are the ones ...
- 2,229
4
votes
Creating 3D Mesh from stl files with gmsh
I am not entirely sure what is going wrong in your version of the command-line approach. However, I think it works on my test STL file (with gmsh 4.0.7) with the following line:
...
- 8,602
4
votes
Accepted
Is there any fundamental difference between meshing for FEM, FVM and FDM?
You are correct that FDM requires structured meshes, so you are restricted to those.
On the other hand FEM and FVM can both do structured meshes as well as unstructured meshes depending on the ...
- 489
4
votes
Accepted
How to find out the difference between a structured and unstructured mesh using the file containing the mesh information?
There are two different types of meshes that are commonly termed "structured":
the points are placed on an equispaced grid; and
the elements have the same connectivity.
Some people might call any ...
- 8,370
4
votes
Accepted
Flux sign and face normal confusion in finite volume method
When dealing with conservation laws like your case, you can often make use of the divergence theorem (as you did). You can then express the fact that the total mass within your integration region is ...
- 2,627
4
votes
Accepted
For traditional FEM and FVM, why can't we use mesh to represent geometry and use the mesh which represent the geometry to do the computation directly?
The underlying problem is that the mesh really isn't the geometry. You want to simulate a bridge? It has a certain geometry, which you can approximate using a mesh, but the mesh is not the exact ...
- 54.2k
4
votes
Convolute a gaussian kernel with a large array of off-grid centroids without looping? (how to make "A Thousand (Gaussian) Points of Light" )
If you simply want to compute the convolution you can construct a Kernel matrix for computation with arbitrary arrangements of Gaussians that do not lie on grid points of the domain where you want to ...
- 725
4
votes
Accepted
Connectivity of octree as grid
The one paper you need to know is the one by Burstedde and collaborators on the implementation of the p4est library: p4est: SCALABLE ALGORITHMS FOR PARALLEL ADAPTIVE
MESH REFINEMENT ON FORESTS OF ...
- 54.2k
4
votes
Interpolation of 1D solution from an original grid to a new grid
A "better technique" is rather subjective. You mean faster, more accurate, easier to program, something else??
Since it's only 1-D, the numerical cost is small (compared to 2D/3D) and there ...
- 206
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